CN106894328B  A kind of processing method of Π shape bondbeam Shear Lag  Google Patents
A kind of processing method of Π shape bondbeam Shear Lag Download PDFInfo
 Publication number
 CN106894328B CN106894328B CN201710090831.6A CN201710090831A CN106894328B CN 106894328 B CN106894328 B CN 106894328B CN 201710090831 A CN201710090831 A CN 201710090831A CN 106894328 B CN106894328 B CN 106894328B
 Authority
 CN
 China
 Prior art keywords
 shape
 displacement
 shear lag
 shear
 bondbeam
 Prior art date
Links
 238000003672 processing method Methods 0.000 title claims abstract description 9
 238000006073 displacement reactions Methods 0.000 claims abstract description 96
 238000005381 potential energy Methods 0.000 claims abstract description 36
 238000010276 construction Methods 0.000 claims abstract description 25
 239000011159 matrix materials Substances 0.000 claims abstract description 23
 239000002131 composite materials Substances 0.000 claims abstract description 20
 229910000831 Steel Inorganic materials 0.000 claims description 59
 239000010959 steel Substances 0.000 claims description 59
 239000004567 concrete Substances 0.000 claims description 43
 230000001264 neutralization Effects 0.000 claims description 14
 230000003068 static Effects 0.000 claims description 8
 238000010008 shearing Methods 0.000 claims description 5
 230000001808 coupling Effects 0.000 claims description 3
 238000010168 coupling process Methods 0.000 claims description 3
 238000005859 coupling reactions Methods 0.000 claims description 3
 238000005452 bending Methods 0.000 abstract description 24
 238000004458 analytical methods Methods 0.000 abstract description 11
 230000035772 mutation Effects 0.000 abstract description 2
 230000035882 stress Effects 0.000 description 22
 238000000034 methods Methods 0.000 description 12
 230000000694 effects Effects 0.000 description 11
 239000000203 mixtures Substances 0.000 description 10
 230000015572 biosynthetic process Effects 0.000 description 5
 238000005755 formation reactions Methods 0.000 description 5
 230000000875 corresponding Effects 0.000 description 4
 238000010586 diagrams Methods 0.000 description 4
 238000004364 calculation methods Methods 0.000 description 3
 239000000463 materials Substances 0.000 description 3
 238000009434 installation Methods 0.000 description 2
 238000006467 substitution reactions Methods 0.000 description 2
 239000000725 suspensions Substances 0.000 description 2
 210000003027 Ear, Inner Anatomy 0.000 description 1
 241000736192 Ostrya virginiana Species 0.000 description 1
 238000004422 calculation algorithm Methods 0.000 description 1
 238000006243 chemical reactions Methods 0.000 description 1
 230000001419 dependent Effects 0.000 description 1
 230000004069 differentiation Effects 0.000 description 1
 229920001971 elastomers Polymers 0.000 description 1
 239000000806 elastomers Substances 0.000 description 1
 238000005516 engineering processes Methods 0.000 description 1
 239000010950 nickel Substances 0.000 description 1
 238000005457 optimization Methods 0.000 description 1
 239000011513 prestressed concrete Substances 0.000 description 1
 239000011150 reinforced concrete Substances 0.000 description 1
 239000004576 sand Substances 0.000 description 1
 238000004088 simulation Methods 0.000 description 1
 239000002689 soil Substances 0.000 description 1
 239000010936 titanium Substances 0.000 description 1
Classifications

 E—FIXED CONSTRUCTIONS
 E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
 E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
 E01D11/00—Suspension or cablestayed bridges
 E01D11/04—Cablestayed bridges

 E—FIXED CONSTRUCTIONS
 E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
 E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
 E01D19/00—Structural or constructional details of bridges
 E01D19/12—Grating or flooring for bridges; Fastening railway sleepers or tracks to bridges

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06F—ELECTRIC DIGITAL DATA PROCESSING
 G06F30/00—Computeraided design [CAD]
 G06F30/10—Geometric CAD
 G06F30/13—Architectural design, e.g. computeraided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads

 E—FIXED CONSTRUCTIONS
 E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
 E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
 E01D2101/00—Material constitution of bridges
 E01D2101/20—Concrete, stone or stonelike material
 E01D2101/24—Concrete

 E—FIXED CONSTRUCTIONS
 E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
 E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
 E01D2101/00—Material constitution of bridges
 E01D2101/30—Metal

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06F—ELECTRIC DIGITAL DATA PROCESSING
 G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
 G06F2119/06—Power analysis or power optimisation
Abstract
Description
Technical field
The invention belongs to bridge construction control technical fields, and in particular to one kind Π shape in CONSTRUCTION OF CABLESTAYED BRIDGE control process The processing method of bondbeam Shear Lag Effect.
Background technique
With the rapid development of the national economy, the requirement to cablestayed bridge span ability is higher and higher, therefore in the design more More Π shape bondbeams using steel truss girder, prestressed concrete П ellbeam or " double Isteel+concrete slabs ".Π shape bondbeam Can give full play to two kinds of materials of steel and concrete respectively advantage and convenient for construction, have extensive development prospect.However, Π shape knot " the ratio of width to height " for closing beam is relatively very big, and top plate width is cut much larger than top plate width between box beam median ventral plate between especially two webs Power hysteresis effect is the important mechanical characteristics of this opening wide cut thin walled beam.It is used in the higher cablestayed bridge of Construction control difficulty When Π shape bondbeam, accurately influence of the analysis Shear Lag to girder bending stiffness and section stress is extremely important, concerning knot Structure safety and control precision.
For the research of thin walled beam Shear Lag Effect, there is significant progress.《It highway reinforced concrete and answers in advance Power concrete bridges and culverts design specification》(JTG D622004, P16~18) 4.2.2 and 4.2.3 articles respectively cut T shape and boxshaped The Studies On Effective Width of face beam is provided, the influence of Shear Lag is considered with this, however this method is primarily adapted for use in knot State is configured with the simple bridge type of stress fixation into the bridge stage, can not really be reflected in complicated bridge type construction dynamic process Structural form and the changing rule that is influenced by Shear Lag of stress.
105046027 A of Chinese patent literature CN discloses a kind of more ribbed tee girder bridge sections on November 11st, 2015 Optimum design method, it establishes the control differential equation and nature of more ribbed tee girder bridges based on minimum potential energy principal Boundary condition considers that more ribbed beam bridge Shear Lag Effects, shear lag warping stress selfbalancing condition and hophornbeam Xin Ke cut shear The influence of the factors such as shape to the mechanical analysis that the class formation is refined, and then is made by the selection of rational cross section size more Ribbed beam bridge is in good mechanical state.105243236 A of Chinese patent literature CN discloses one on January 13rd, 2016 Kind boxgirder bridge section design optimization method, this method consider the shadow of the factors such as boxgirder shear lag and sheardeformable effect It rings, acquires the potential energy of deformation and kinetic energy of boxgirder first, and then obtain structural dynamic control differential side using Hamiton's principle Journey and natural boundary conditions.But the shortcomings that the two patents, is：They are confined to Constructional differential equation and side derived from energy method Boundary's condition still can not be applied to the analysis of Shear Lag of complicated Construction of CableStayed Bridges.
" bending the finite segment method that box beam Shear Lag calculates ", sieve flag, Foshan Univ.'s journal, the 2nd phase of volume 12, the Page 23~31, one kind are described in April, 1994 under Compactbending Load collective effect, using the homogeneous solution of control differential equation as cutting The stagnant warp displacement mode of power, the finite segment method calculated suitable for cablestayed bridge Shear Lag." the one of boxgirder Analysis of Shear Lag Effect Tie up FInite Element and its application ", Zhang Yuanhai, Wang Lailin, Li Qiao, civil engineering journal, the 8th phase of volume 43, page 44~50, In August, 2010 describes a kind of improved the finite segment method, can by introducing shear lag Generalized Moment and warpage geometrical property Analyze the Girder with Shear Lag Effect of the labyrinths such as box girder with variable cross section and special support continuous box girder.But these methods are equal on each node Only consider that a Shear Lag freedom degree, Shear Lag freedom degree refer to the independent node position introduced for describing Shear Lag state It moves, sieve, two people only consider a Shear Lag freedom degreeIt cannot be adapted to the boundary condition of various analysis of Shear Lag.
Bondbeam, which is girder steel and concrete slab, combines the common stress in section formed, compatibility of deformation by shear connector A kind of composite structure, also known as combination beam (highway Railway System habit uses " bondbeam ", other professions claim " combination beam " more).Such as figure Shown in 1, Π shape bondbeam refers to the combination beam that concrete slab 1 and girder steel 2 are combined on cross section with the shape of alphabetical Π.
For П shape combination girder stayedcable bridge, (suspension cable anchor point bias and in advance answered since girder bears concentrated bending moment Power anchorage is eccentric) and the Shear Lag displacement boundary conditions mutation problems that generate, load and Shear Lag displacement in dynamic process of constructing The continually changing problem of boundary condition, the above method can not be fully solved.Since the prior art is confined under single operating condition Simple structure analysis, not can solve in CONSTRUCTION OF CABLESTAYED BRIDGE dynamic process because there are the construction errors caused by Shear Lag Effect to ask Topic.
Summary of the invention
For technical problem of the existing technology, the present invention provides a kind of processing sides of Π shape bondbeam Shear Lag Method, it can consider in real time influence of the Shear Lag to girder stress and deformation in simulation CONSTRUCTION OF CABLESTAYED BRIDGE dynamic process, improve The accuracy of Π shape bondbeam Construction of CableStayed Bridges.
It is realized the technical problem to be solved by the present invention is to technical solution in this way, it includes
Step 1, according to the design feature of Π shape composite beam section, construction is suitable for the Shear Lag warpage position of Π shape bondbeam Move function u_{i}(x, y) is：
In formula,For Shear Lag displacement；
h_{i}For the distance of concrete slab or the middle plane of steel beam flange to Π shape composite beam section neutral axis；
ζ_{i}For the correction factor for considering sheardeformable influence degree, takes 1to consider, takes 0not consider；
B is the 1/2 of two steel beam web plate spacing；
Subscript i=1,2,3,4 indicate respectively tetra regions 1#, 2#, 3#, 4# of Π shape composite beam section：
The region 1# is the half of clear distance range inner concrete plate between two girder steels；
The region 2# be girder steel top flange top concrete plate and overhanging unilateral concrete slab and；
The region 3# is girder steel lower flange；
The region 4# is girder steel top flange；
ξ_{i}For the width correction factor, the respectively ratio of the width and b of 1#~4# zone plate；
Step 2, according to the Shear Lag warp displacement function u established in step 1_{i}(x, y) calculates total gesture of Π shape bondbeam It can Π；
Step 3, it according to the total potential energy Π acquired in step 2, is expressed by minimum potential energy principal foundation with variational form quiet Equilibrium equation, the equation of static equilibrium are using displacement function as fundamental unknown variables；
Step 4, the equation of static equilibrium is solved, each node introduces the positional displacement interpolation function of two Shear Lag freedom degrees, right The resulting equation of static equilibrium of step 3 carries out discretization, is deformed into using generalized nodal displacement as the balance side of fundamental unknown variables Journey obtains the element stiffness matrix [K] for considering that Shear Lag influences.
Particularly, in step 2, the total potential energy of Π shape bondbeam is：
In above formula,For Shear Lag displacementBelong to angular displacement；For Shear Lag displacementFirst derivative, belong to Generalized displacement.
Technical effect of the invention：
Since the present invention proposes reasonable Shear Lag warp displacement mode by the crosssection analysis to Π shape bondbeam, and Intercoupling between vertical displacement and Shear Lag displacement is considered, uses two Shear Lag freedom degrees at each section of Π shape bondbeam (i.e.With), it can adapt to different Shear Lag displacement boundary conditions.In addition, all modeling process all programs Change, convenient for operation and programming, greatly reduced artificial calculation amount, the meter of Π shape bondbeam Shear Lag is realized by computer It calculates, the changing rule of Π shape girder Shear Lag and influence in complicated CONSTRUCTION OF CABLESTAYED BRIDGE dynamic process is studied with this.
So it is an advantage of the invention that：Different Shear Lag displacement boundaries is adapted to, Π shape combination girder stayedcable bridge is improved The accuracy of work progress more meets reality to the prediction result of girder stress and deformation.
Detailed description of the invention
Detailed description of the invention of the invention is as follows：
Fig. 1 is the structural schematic diagram of Π shape composite beam section；
In Fig. 1：1. concrete slab；2. girder steel；
Fig. 2 is the direct stress distributional assumption figure of one unit of Π shape bondbeam of the present invention；
Fig. 3 is the overall structure diagram of cablestayed bridge mainbeam；
The structural parameters that Fig. 4 is Fig. 1 mark figure；
Fig. 5 is the Stayed Cable Bridge of one embodiment across layout drawing；
Fig. 6 is that the cablestayed bridge cross sectional dimensions of one embodiment marks figure；
Fig. 7 is the stagnant coefficient of The East Pagoda end bay auxiliary pier pier top section shear in embodiment with Construction State variation diagram；
Fig. 8 is the schematic diagram of CONSTRUCTION OF CABLESTAYED BRIDGE sequence and section number, beam element structure；
Fig. 9 is that the actual measurement of The East Pagoda end bay auxiliary pier pier top section, theoretical stress compare after the installation of 10# floorings in embodiment Figure；
Figure 10 is the absolute altitude difference curve graph of girder after 14# cable tension in embodiment.
Specific embodiment
Present invention assumes that the direct stress of one unit of Π shape bondbeam is distributed as shown in Fig. 2, establishing unit coordinate in Fig. 2 System's (or being local coordinate system), it is vertically the direction z that axial (length direction), which is the direction x, and laterally (width direction) is the direction y. The maximum difference of shear rotation angle is shown in Fig. 2
As shown in figure 3, cablestayed bridge mainbeam is that unit one as shown in Figure 2 spells successively, it, can for overall structure Establish a global coordinate system (or being structure coordinate system).In global coordinate system, along bridge to (also known as vertical bridge is to length side To) it is Xdirection, direction across bridge (width direction) is Ydirection, is vertically Zdirection to (short transverse).
The present invention be directed to a kind of beam elements, and mainly the formation of unit is derived and described, therefore need to be to unit coordinate System is arranged.Structure coordinate system can be different with the difference of different software and reckoner, only relate to the conversion of finite element coordinate Problem, not within the scope of creation of the invention.
Present invention will be further explained below with reference to the attached drawings and examples, and the present invention includes the following steps：
Step 1：The characteristics of being constructed according to Π shape composite beam section  concrete slab width is much larger than girder steel between two girder steels With the width on the concrete edge of a wing on girder steel, during Π shape combination beam deformed, concrete slab is due to sheardeformable Caused by shear lag phenomenon it is more significant for the concrete edge of a wing；Simultaneously as concrete material is a kind of non Uniformly, anisotropic material with complex discusses merely that the stress of certain point is not anticipate from microscale in the actual process It is adopted and unnecessary, and the mean stress of the macroregions big relative to aggregate size several times is discussed and just more meets reality.It is based on These characteristics, for the Π shape bondbeam that girder steel and concrete slab are well combined, bond area is smaller, region internal stress level Be not much different, it is believed that the stagnant influence very little of the region internal shear force and ignore its influence, so, this step proposition be suitable for Π shape knot Close the Shear Lag warp displacement function u of beam_{i}(x,y)：Only consider girder steel between clear distance range inner concrete plate shear lageffect, suddenly The slightly influence of remaining each section Shear Lag.
Notation convention, and selected Shear Lag warp displacement mould are carried out to the structure composition of Π shape bondbeam cross section first Formula.For convenience of description, Π shape composite beam section is divided into 4 regions, as shown in Figure 1：
The region 1#  the half of clear distance range inner concrete plate between two girder steels, subscript are indicated with " 1 "；
The region 2#  girder steel top flange top concrete plate and overhanging unilateral concrete slab and, subscript use " 2 " indicate；
The region 3#  girder steel lower flange, subscript are indicated with " 3 "；
The region 4#  girder steel top flange, subscript are indicated with " 4 "；
For steel beam web plate, the subscript of dependent crosssection geometrical property is indicated with " w ".
As shown in figure 4, taking the 1/2 of two steel beam web plate spacing to be used as width b, then ξ_{i}B (i=1,2,3,4) is the area 1#~4# Domain plate width, wherein ξ_{i}The respectively ratio of the width and b of 1#~4# zone plate, referred to as the width correction factor.In Fig. 4, t_{1}、 t_{2}、t_{3}、t_{4}The respectively thickness of 1#~4# zone plate plate, h_{1}、h_{2}Plane is to Π shape knot respectively in the concrete slab of the region 1#, 2# Close the distance of beam section neutral axis；h_{3}、h_{4}For the distance of plane in the upper and lower edge of a wing of girder steel to Π shape composite beam section neutral axis.
It introduces axial displacement u=u (x), vertical displacement v=v (x) and Shear Lag warp displacement u_{i}The three broad sense positions (x, y) It moves.Direct stress distribution as shown in Figure 2, ignores the shear lageffect in the region 2#~4#, only considers the shear lageffect in the region 1#, It is, by u_{1}(x, y) is assumed to 3 parabolic distributions, and u_{2}(x,y)、u_{3}(x,y)、u_{4}(x, y) is taken as horizontal linear, i.e.,
In formula (1),For the maximum difference of shear rotation angle, also known as Shear Lag is displaced；
h_{i}For the distance of concrete slab or the middle plane of steel beam flange to Π shape composite beam section neutral axis；
ζ_{i}The correction factor for considering sheardeformable influence degree, only has herein：1considers that 0does not consider.
Formula (1) be Π shape bondbeam Shear Lag warp displacement mode, it should be noted that dv/dx withIt is contrary sign, in 1# Region and the region 2# intersection displacement components u_{i}(x, y)=h_{i}Dv/dx is maximum value (region 1# and the region 2# intersection u_{1}(x, y)= u_{2}(x,y))。
Web meets the plane crosssection assumption of General beam theory under symmetric curvature load action.It only relates to herein longitudinal curved Bent deformation potential and axial deformation deformation potential, and transverse curvature deformation potential is negligible, the vertical extruding of upper lower flange ε_{z}, the outofplane sheardeformable γ in the edge of a wing_{xz}, γ_{yz}And transverse curvature, transverse strain belong to micro, can be neglected.
Step 2：According to the Shear Lag warp displacement function u established in step 1_{i}(x, y) calculates total potential energy of structural system Π includes：Load potential energy V, girder axial deformation deformation potential U_{A}, girder Bending Deformation potential energy (U_{w}+U_{c}+U_{s}), wherein U_{w}For steel Web Bending Deformation potential energy, U_{c}For concrete slab Bending Deformation potential energy, U_{s}For steel beam flange Bending Deformation potential energy.The axis Refer to that displacement of the neutral plane along unit axis, the bending deformation refer to corner of the cross section around neutral axis to deformation.
Various potential energy are calculated separately below：
(1) when beam is by " unit evenly load " and " node load ", load potential energy V is
In formula (2), { Δ } is modal displacement array, and { F } is nodal load matrix, and q (x) is unit vertical uniform load, l For element length.
(2) girder axial deformation deformation potential U_{A}
In formula (3), E_{c}For modulus of elasticity of concrete, E_{s}For the elasticity modulus of steel；U '=u ' (x) is axial displacement u=u (x) First derivative, A_{c}For concrete slab area of section, (section is the cross section of beam element, for one dimension finite element, is pressed Agreement geometric characteristics refer in particular to the geometric characteristics in cell crosssection), A_{s}For girder steel area of section, A=E is enabled_{c}A_{c}/ E_{s}+A_{s}, have：
(3) girder Bending Deformation potential energy
Steel beam web plate
In formula (5), I_{w}It is web to the moment of inertia of Π shape composite beam section neutral axis, v " is the second order of vertical displacement v=v (x) Derivative.
Concrete slab
In formula (6), G_{c}For the modulus of shearing of concrete, U_{1}For the Bending Deformation potential energy of the region 1# concrete slab, U_{2}For the area 2# The Bending Deformation potential energy of domain concrete slab.
Steel beam flange
In formula (7), G_{s}For the modulus of shearing of steel, U_{3}For the Bending Deformation potential energy of the region 3# girder steel lower flange, U_{4}For the region 4# The Bending Deformation potential energy of girder steel top flange.
In formula (6) and formula (7), t_{i}For the thickness of the region i# plate, ε_{i}、γ_{i}Respectively
Formula (8) is substituted into formula (6), formula (7) respectively, is had
1. concrete slab Bending Deformation potential energy U_{c}
It enablesSimultaneously
I_{ca}=I_{1}+I_{2},I_{cb}=ζ_{1}I_{1},
It can obtain
In formula (12),Referred to as " generalized nodal displacement " can describe independent degree on cell node in a broad sense Variable, being corresponding to it has " generalized nodal force ".It is about the reasons why " generalized nodal displacement " formation：
Any point in twodimensional surface should only there are two independent modal displacement u, v (the two displacements are displacements of the lines), But for member structure, corner displacement θ (i.e. angular displacement) is introduced on node, to describe the bending change of rod piece, so There are 3 displacement components us, v, θ, and θ=dv/dx=v on each node of general plane bar element^{/}, this is that civil engineering basis is known Know.
In order to describe the shear lageffect of thinwalled bar, the present invention abovementioned bar unit on the basis of introducing two changes again Measure φ andTo describe shear lageffect, wherein φ is the maximum difference of shear rotation angle, identical as the dimension of rotational angle theta, is belonged to logical Normal " angular displacement " scope；And φ isFirst derivative, do not correspond to a certain specific change in displacement of bar element, belong to wide The scope that adopted position is moved.Mathematically, it is the displacement state in description bar unit vertical plane, can theoretically following variables is taken to make For modal displacement：
V, θ=v^{/}、v^{//}、v^{///}、……、v^{(n)}
But only the first two displacement is for specific change in displacement, v  displacement of the lines, θ=v^{/} angular displacement, and thereafter V^{//}、v^{///}、……、v^{(n)}It is only mathematically significant, and be corresponding to it without actual displacement, therefore referred to as generalized displacement.
2. steel beam flange Bending Deformation potential energy U_{s}
It enablesSimultaneously
I_{sa}=2I_{3}+2I_{4},I_{sb}=I_{sc}=I_{sd}=0 (15)
It can obtain
It enables
It can obtain
According to formula (4), formula (5) and formula (18) it is found that Π shape bondbeam deformation potential U is
In formula (19), I=I_{w}+I_{fa}。
By formula (2) and formula (19) it is found that the total potential energy Π of Π shape bondbeam is
In formula (20),
V is load potential energy；
U is Π shape bondbeam deformation potential (including girder axial deformation deformation potential U_{A}, steel beam web plate Bending Deformation potential energy U_{w}, concrete slab Bending Deformation potential energy U_{c}With steel beam flange Bending Deformation potential energy U_{s})；
A=E_{c}A_{c}/E_{s}+A_{s}；
E_{s}For the elasticity modulus of steel；
E_{c}For modulus of elasticity of concrete；
A_{c}For concrete slab area of section；
A_{s}For girder steel area of section；
L is element length；
U '=u ' (x) is the first derivative of axial displacement u=u (x)；
V (x) is vertical displacement, and ν " is the second dervative of vertical displacement v=v (x)；
For Shear Lag displacement For Shear Lag displacementFirst derivative；
{ Δ } is modal displacement array, and { F } is nodal load matrix, and q (x) is unit vertical uniform load；
G_{s}For the modulus of shearing of steel；
B is the 1/2 of two steel beam web plate spacing；
I=I_{w}+I_{fa}
I_{w}It is web to the moment of inertia of Π shape composite beam section neutral axis；
I_{ca}=I_{1}+I_{2}, I_{cb}=ζ_{1}I_{1},
I_{sa}=2I_{3}+2I_{4}, I_{sb}=I_{sc}=I_{sd}=0
t_{1}、t_{2}、t_{3}、t_{4}The respectively thickness of 1#~4# zone plate plate；
h_{1}、h_{2}Respectively in the concrete slab of the region 1#, 2# plane to Π shape composite beam section neutral axis distance；
h_{3}、h_{4}Respectively in the steel beam flange of the region 3#, 4# plane to Π shape composite beam section neutral axis distance；
ξ_{i}B (i=1,2,3,4) is the region 1#~4# plate width.
Step 3：According to minimum potential energy principal, under external force, the elastomer in stability is meeting side In all displacements of boundary's condition, unique one group of displacement there are in fact, this group displacement can make total potential energy of whole system most Small, i.e. the first variation of the total potential energy of system should be zero
δ Π=δ (U+V)=0 (21)
Formula (20) are substituted into, can be obtained
Formula (22) is the total potential energy Π acquired in foundation step 2, and is expressed by minimum potential energy principal foundation with variational form The equation of static equilibrium, the equation be with u (x), v (x) andThree displacement functions are as fundamental unknown variables.
It should be noted that the displacement function of selection must meet displacement boundary conditions on being displaced known boundary, Face force boundary is then not necessarily to consider, because of its automatic satisfaction.
Step 4：In meeting cablestayed bridge under Shear Lag displacement boundary conditions sudden change conditions caused by concentrated bending moment, step is solved Rapid 3 resulting equilibrium equation.
Beam element structure as shown in Figure 8：According to the requirement of beam section finite element, need to serve as reasons overall structure discretization " section The finite element model of point+beam element " composition, also known as finite element grid, each beam element have 2 nodes  the end i and the end j.This In step, each node introduces two Shear Lag freedom degrees (i.e.With) positional displacement interpolation function.
It is introduced into positional displacement interpolation function and modal displacement (10 displacement parameters i.e. in modal displacement array { Δ }), to formula (22) discretization is carried out.Axial displacement u uses linear interpolation, vertical displacement v and Shear Lag displacement3 Hermite is selected to insert Value, shape function use [N respectively_{u}]、[N_{v}] andIt indicates
U=[N_{u}] { Δ }, v=[N_{v}]{Δ},
In formula (23)
Modal displacement array { Δ } includes 10 displacement parameters, is
Nodal load matrix corresponding with formula (26) is
{ F }=[N_{i} Q_{i} M_{i} S_{i} T_{i} N_{j} Q_{j} M_{j} S_{j} T_{j}]^{T} (27)
In formula (26) and formula (27), i, j are the end i and the end j of beam element；u_{i}And u_{j}For axial displacement；v_{i}And v_{j}For vertical position It moves；θ_{i}And θ_{j}For angular displacement；WithFor the generalized shear stagnating bit shifting parameter at unit both ends；N_{i}And N_{j}For axle power；Q_{i}With Q_{j}For shearing；M_{i}And M_{j}For moment of flexure；S_{i}、T_{i}、S_{j}And T_{j}Respectively withWithThe corresponding stagnant unit node of generalized shear Power.
It brings formula (23) into formula (22), has
Because node virtual displacement { δ Δ } is arbitrary value, have
It enables
Then formula (29) is rewritten as the equilibrium equation using generalized nodal displacement as fundamental unknown variables：
In formula (31), [K]=[K_{e}]+[K_{s}] it is the element stiffness matrix for considering Shear Lag and influencing；{ Δ } is modal displacement column Battle array；{ F } is node load array；For unit evenly load array.
[K_{e}] be existing elementary beam element elastic stiffness matrix
Shear Lag and curved coupling influence are by [K_{s}] indicate
Formula (24), formula (25) are substituted into formula (30), obtain considering the element stiffness square that Shear Lag influences under unit coordinate system Battle array [K] be：
Finally, being coordinately transformed and always rigid group using element stiffness matrix of the existing finite element method to formula (34) Collection, to solve the equilibrium equation based on modal displacement.
Formula (31) is unit analysis as a result, element stiffness matrix therein [K] (abbreviation Dan Gang) is a singular matrix, nothing Method solves.To acquire modal displacement, global analysis is carried out, needs to be coordinately transformed to obtain under global coordinate system by formula (31) Dan Gang [K], and a group collection is carried out to each unit stiffness matrix and obtains the global stiffness matrix of bed rearrangement cablestayed bridge, could formed whole The nodal equilibrium equation of body structure, the equation are exactly the equilibrium equation based on modal displacement that can be solved, and then it is total to form structure Body stiffness matrix (referred to as total rigid) and its equilibrium equation, this belongs to the generalized flowsheet of finite element method, is obtained using existing algorithm As a result.
Embodiment
Fig. 5 is a Stayed Cable Bridge across layout drawing, and Fig. 6 is cablestayed bridge cross sectional dimensions mark figure.It is provided by Fig. 5 and Fig. 6 Cablestayed bridge span distribution and section parameter are shown in Table 1, wherein each beam section steel plate plate dimensions is shown in Table 2.
1 Stayed Cable Bridge of table is across size and section parameter
Each beam section steel plate board dimensions (mm) of table 2
Explanation：2 central sill segment type of table is numbered for being identified to different types of segment.One CONSTRUCTION OF CABLESTAYED BRIDGE circulation One segment of middle formation, and all parts size of each segment can change with demand, in order to each type of segment It is identified, introduces beam section type number and the beam section with identical size is numbered.
Each beam section cross section geometric characteristic parameter is calculated according to formula (17)：A, I, I_{fb}, I_{fc}And I_{fd}, the results are shown in tables 3.It is mixed Solidifying soil elasticity modulus is E_{c}=35500MPa, steel elasticity modulus are E_{s}=210000MPa, the half of steel beam web plate spacing are b= 12m。
Each beam section cross section geometric characteristic parameter (mm of table 3^{2},mm^{4})
By the cross section geometric characteristic parameter in table 3, modulus of elasticity of concrete E_{c}, steel elastic modulus E_{s}And steel beam web plate Half b and unit computational length l of spacing substitute into the element stiffness matrix [K] for considering that Shear Lag influences, and can acquire each beam section and consider The element stiffness matrix that Shear Lag influences.
Show applying in cablestayed bridge by the sunykatuib analysis to practical Π shape combination girder stayedcable bridge project construction dynamic process During work, the stress behavior of Π shape bondbeam shows apparent shear lag phenomenon.It should be noted that arbitrary section For Shear Lag it is not unalterable, but as the propulsion of work progress and the differentiation of structural form constantly change, such as Fig. 7 It is shown.Abscissa indicates that construction procedure number, ordinate are shear lag coefficient λ in Fig. 7, and the calculating of shear lag coefficient λ is as follows：
In formula (35), σ_{x}、Indicate cross section stresses,For elementary beam element section stress, σ_{x}Consider for the present invention Section stress after shear lageffect.
In formula (36), M (x) is section turn moment.In the region 1# and the region 2# intersection (y=ξ_{1}B) shear lag coefficient is
It is in concrete slab midpoint (y=0) shear lag coefficient
It will consider that element stiffness matrix [K] the substitution general finite element program that Shear Lag influences calculates, acquire broad sense Modal displacementAnd formula (38), (39) are substituted into, λ is acquired to calculate_{w}And λ_{c}。
As seen from Figure 7, in the construction process, the stagnant change for not only numerically having size of same section shear, in mode It is upper that there are also the Alternate Phenomenons of positive and negative Shear Lag.
As shown in figure 8, Π shape combination girder stayedcable bridge is assembled, the bridge surface in bridge project of the segment of segment one The segment Ta Chu is about set to 0#, then with the formation of girder, newlyincreased segment successively according to 1#, 2#, 3# ..., i# compiled Number, this is the general agreement in science of bridge building.
For the construction effect for verifying present method invention, for The East Pagoda end bay auxiliary pier pier top section as shown in Figure 5, applying Work stage 10# floorings installation after, with the result of General beam theory calculated result, calculated result of the invention and actual test by Shown in Fig. 9, ordinate is section stress in Fig. 9, and abscissa is direction across bridge coordinate, is found out by Fig. 9：Present method invention is calculated Section theoretical stress closer to actual measured results, it is higher than the accuracy that application General beam theory calculates.
The Stress calculation of General beam theory is according to obtained by formula (36), and Stress calculation of the invention is according to obtained by formula (37).By The coupling influence of Shear Lag Yu girder bending stiffness has been fully considered in the present invention, so can inquire into Π shape bondbeam oblique pull Influence of the Shear Lag to girder bending stiffness during bridge construction, to realize linear accurate of Construction of CableStayed Bridges middle girder Control.
Figure 10 is the absolute altitude difference curve graph of girder after 14# cable tension.14# dragline is the longest suspension cable in east, Xi Ta, Absolute altitude difference is to calculate height value (specially by the present invention：It will consider that element stiffness matrix [K] substitution that Shear Lag influences is general Finite element program is calculated, and acquires node theory vertical displacement v), then subtracted each other with the absolute altitude value of actual measurement and found out.
Found out by Figure 10：Maximum cantilever state after 14# cable tension, the theoretical absolute altitude calculated using present method invention And the difference very little of measured value is no more than 3cm, and result is positive and negative staggeredly shows certain randomness and unsystematic defect, table The bright present invention accurately reflects the case where Π shape bondbeam actual loading deformation.
Claims (5)
Priority Applications (1)
Application Number  Priority Date  Filing Date  Title 

CN201710090831.6A CN106894328B (en)  20170220  20170220  A kind of processing method of Π shape bondbeam Shear Lag 
Applications Claiming Priority (1)
Application Number  Priority Date  Filing Date  Title 

CN201710090831.6A CN106894328B (en)  20170220  20170220  A kind of processing method of Π shape bondbeam Shear Lag 
Publications (2)
Publication Number  Publication Date 

CN106894328A CN106894328A (en)  20170627 
CN106894328B true CN106894328B (en)  20181123 
Family
ID=59184841
Family Applications (1)
Application Number  Title  Priority Date  Filing Date 

CN201710090831.6A CN106894328B (en)  20170220  20170220  A kind of processing method of Π shape bondbeam Shear Lag 
Country Status (1)
Country  Link 

CN (1)  CN106894328B (en) 
Families Citing this family (3)
Publication number  Priority date  Publication date  Assignee  Title 

CN107700336A (en) *  20171023  20180216  沈阳建筑大学  A kind of determination method of Main Girder of Concrete Cablestayed Bridge construction stage Shear Lag 
CN109252441B (en) *  20180919  20200616  重庆交通大学  Analysis method for shear hysteresis effect of variable crosssection box beam 
CN110032829B (en) *  20190517  20201110  成都理工大学  Stress calculation method of steelconcrete composite beam 
Citations (6)
Publication number  Priority date  Publication date  Assignee  Title 

JPH0820910A (en) *  19940705  19960123  Kajima Corp  Construction method of pc cable stayed bridge 
CN102191750A (en) *  20100310  20110921  重庆交通大学  Construction method for waterproof isolation structure of anchor plate of cablestayed bridge by adopting steelconcrete composite beam 
KR101200563B1 (en) *  20080714  20121113  한국건설기술연구원  A Steel Composite Bridge Having Steel Plates Connected by Using Concrete Cross Beams and Its Constructing Method 
CN104294748A (en) *  20140923  20150121  同济大学  Joint section structure for hybrid beam cablestayed bridge and construction method thereof 
WO2016023462A1 (en) *  20140815  20160218  中交第二航务工程局有限公司  Glued joint connecting method for steelconcrete composite beam of cablestayed bridge 
CN105544373A (en) *  20151207  20160504  清华大学  Steel boxconcrete composite girder for longspan cablestayed bridge and construction method 

2017
 20170220 CN CN201710090831.6A patent/CN106894328B/en active IP Right Grant
Patent Citations (6)
Publication number  Priority date  Publication date  Assignee  Title 

JPH0820910A (en) *  19940705  19960123  Kajima Corp  Construction method of pc cable stayed bridge 
KR101200563B1 (en) *  20080714  20121113  한국건설기술연구원  A Steel Composite Bridge Having Steel Plates Connected by Using Concrete Cross Beams and Its Constructing Method 
CN102191750A (en) *  20100310  20110921  重庆交通大学  Construction method for waterproof isolation structure of anchor plate of cablestayed bridge by adopting steelconcrete composite beam 
WO2016023462A1 (en) *  20140815  20160218  中交第二航务工程局有限公司  Glued joint connecting method for steelconcrete composite beam of cablestayed bridge 
CN104294748A (en) *  20140923  20150121  同济大学  Joint section structure for hybrid beam cablestayed bridge and construction method thereof 
CN105544373A (en) *  20151207  20160504  清华大学  Steel boxconcrete composite girder for longspan cablestayed bridge and construction method 
NonPatent Citations (1)
Title 

"连续刚构箱梁剪力滞效应分析";李兴坤;《河南城建学院学报》;20120731;第21卷(第4期);第810页 * 
Also Published As
Publication number  Publication date 

CN106894328A (en)  20170627 
Similar Documents
Publication  Publication Date  Title 

Megson  Structural and stress analysis  
Oehlers et al.  Composite steel and concrete structures: fundamental behaviour: fundamental behaviour  
Hambly  Bridge deck behaviour  
Dongsheng et al.  Experimental and analytical study on the nonlinear bending of parallel strand bamboo beams  
Varghese  Advanced reinforced concrete design  
Natário et al.  Shear strength of RC slabs under concentrated loads near clamped linear supports  
Lourenço  Recent advances in masonry modelling: micromodelling and homogenisation  
CN104166792B (en)  A kind of prestressed concrete continuous rigidframed bridge temperature action finite element method  
Nie et al.  Experimental and analytical study of prestressed steel–concrete composite beams considering slip effect  
Reyes et al.  An embedded cohesive crack model for finite element analysis of brickwork masonry fracture  
Malm  Shear cracks in concrete structures subjected to inplane stresses  
CN104992019B (en)  A kind of simplification design method of Extralong Railway Bridge beam nonfragment orbit gapless track  
Kalantari et al.  An approximate method for dynamic analysis of skewed highway bridges with continuous rigid deck  
Guezouli et al.  Numerical analysis of frictional contact effects in pushout tests  
Chen et al.  Flexural behaviour of rebarreinforced ultrahighperformance concrete beams  
Almeida et al.  Punching behaviour of RC flat slabs under reversed horizontal cyclic loading  
Chiewanichakorn et al.  Effective flange width definition for steel–concrete composite bridge girder  
Ritter et al.  Centrifuge modelling of building response to tunnel excavation  
Muttoni et al.  Levelsofapproximation approach in codes of practice  
Kong et al.  New strategy of substructure method to model longspan hybrid cablestayed bridges under vehicleinduced vibration  
Ren et al.  Field load tests and numerical analysis of Qingzhou cablestayed bridge  
Berczyński et al.  Experimental verification of natural vibration models of steelconcrete composite beams  
Zhang et al.  Mesoscale partitioned analysis of brickmasonry arches  
Nana et al.  Experimental and numerical modelling of shear behaviour of fullscale RC slabs under concentrated loads  
Mistler et al.  Modelling methods of historic masonry buildings under seismic excitation 
Legal Events
Date  Code  Title  Description 

PB01  Publication  
PB01  Publication  
SE01  Entry into force of request for substantive examination  
GR01  Patent grant  
GR01  Patent grant 